Finite Group Databasebeta

← #19137733

Subgroups — #19137733

Order 5504.

688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063293C211yesmaximal, characteristic
2#14582802C211yesmaximal, characteristic, complemented
3#14582799C212yesmaximal, complemented
4#14582793C212yesmaximal, complemented
5#14582791C212yesmaximal, complemented
6#14582788C212yesmaximal, complemented
7#14582778C212yesmaximal, complemented
8#14582754C212yesmaximal, complemented
9C43×#386C211yesmaximal, characteristic, complemented
10C24×D43C2211yescharacteristic
11C22×C22⋊D43C2212yes—
12#13063293C418yescomplemented
13C2×C4⋊Dic43C2211yescharacteristic, complemented
14C2×Dic43⋊C4C2212yescomplemented
15C2×C22⋊Dic43C2212yes—
16C2×C22⋊Dic43C2211yescharacteristic
17C2×C22⋊Dic43C2212yescomplemented
18C2×(C2×D43)⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×C4×Dic43C2211yescharacteristic, complemented
24C2×C4×Dic43C2212yescomplemented
25C43⋊#95C2212yescomplemented
26C43⋊#95C2212yescomplemented
27C22×D4×C43C2211yescharacteristic
28C23×C4×C43C2211yescharacteristic, complemented
29C2×C22⋊C4×C43C2212yes—
30C2×C22⋊C4×C43C2211yescharacteristic, complemented
31#95×C43C2212yescomplemented
32C24×C43C2311yescharacteristic
33C24×C43C2311yescharacteristic
34C23×D43—41no—
35C23×D43—41no—
36C23×D43—42no—
37C23×D43—42no—
38C23×D43C2×C414yescomplemented
39C23×D43C2312yes—
40C2×D4×C43—41no—
41C2×D4×C43—41no—
42C2×D4×C43C2×C414yes—
43C22×C4×C43—42no—
44C22×C4×C43—41no—
45C22×C4×C43C2312yes—
46C22×C4×C43C2312yes—
47C22×C4×C43C2311yescharacteristic
48C2×C22⋊D43—42no—
49C2×C22⋊D43—42no—
50C2×C22⋊D43C2×C418yes—
51C22×Dic43C2312yes—
52C22×Dic43C2312yes—
53C22×Dic43C2312yes—
54C22⋊C4×C43—42no—
55C22⋊C4×C43—41no—
56C22⋊Dic43—42no—
57C22⋊Dic43—42no—
58C22⋊Dic43C2×C414yescomplemented
59(C2×D43)⋊C4—42no—
60(C2×D43)⋊C4—42no—
61(C2×D43)⋊C4—42no—
62(C2×D43)⋊C4—42no—
63(C2×D43)⋊C4C2×C418yescomplemented
64C4⋊Dic43—41no—
65Dic43⋊C4—42no—
66C4×Dic43—42no—
67C4×Dic43—41no—
68C23×C43—22no—
69C23×C43—22no—
70C23×C43—21no—
71C23×C43—22no—
72C23×C43—22no—
73C23×C43—21no—
74C23×C43—21no—
75C23×C43—21no—
76C23×C43C22×C412yes—
77C23×C43C22×C412yes—
78C23×C43C2411yescharacteristic
79C22×D43—22no—
80C22×D43—22no—
81C22×D43—22no—
82C22×D43—22no—
83C22×D43—22no—
84C22×D43—22no—
85C22×D43—44no—
86C22×D43—48no—
87C22×D43—48no—
88C22×D43—44no—
89C22×D43—44no—
90C22×D43C22×C414yes—
91D4×C43—44no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—44no—
101C2×C4×C43C22×C412yes—
102C22⋊D43—48no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43C22×C414yes—
112C22×C43—24no—
113C22×C43—22no—
114C22×C43—24no—
115C22×C43—22no—
116C22×C43—42no—
117C22×C43—41no—
118C22×C43—42no—
119C22×C43—41no—
120C22×C43—41no—
121C22×C43—41no—
122C22×C43C23×C411yescharacteristic
123C22×C43H(5,𝔽2)11yescharacteristic
124C22×C43H(5,𝔽2)12yes—
125C22×C43H(5,𝔽2)11yescharacteristic
126C22×C43H(5,𝔽2)12yes—
127C2×D43—24no—
128C2×D43—24no—
129C2×D43—24no—
130C2×D43—416no—
131C2×D43—42no—
132C2×D43—42no—
133C2×D43—42no—
134C2×D43—42no—
135C4×C43—22no—
136C4×C43—42no—
137C4×C43—42no—
138Dic43—24no—
139Dic43—42no—
140Dic43—42no—
141#2375—431nomaximal, Sylow
142C2×C43—42no—
143C2×C43—42no—
144C2×C43#51812yes—
145C2×C43#51811yescharacteristic
146C2×C43#56012yes—
147C2×C43#56011yescharacteristic
148C2×C43H(3,𝔽4)11yescharacteristic
149D43—44no—
150C2×#120—431no—
151#390—431no—
152#390—432no—
153#388—432no—
154#388—432no—
155#388—432no—
156#386—432no—
157#386D4311yescharacteristic, complemented
158#379—432no—
159C43#237511yescharacteristic, complemented, Sylow
160C25—431no—
161C22×D4—432no—
162C22×D4C2×D4311yescharacteristic
163C23×C4C2×D4311yescharacteristic, complemented
164#120—438no—
165C2×C4⋊C4—432no—
166C2×C4⋊C4—431no—
167C2×C22⋊C4—431no—
168C2×C22⋊C4—432no—
169C2×C22⋊C4—432no—
170C2×C22⋊C4—432no—
171C2×C22⋊C4—432no—
172C2×C22⋊C4—432no—
173C2×C22⋊C4—432no—
174C2×C22⋊C4—432no—
175C2×C22⋊C4C2×D4312yes—
176C2×C22⋊C4C2×D4311yescharacteristic, complemented
177C2×C42—432no—
178C2×C42—431no—
179#95—432no—
180#95—432no—
181#95C2×D4312yescomplemented
182C24—432no—
183C24—434no—
184C24—1722no—
185C24—1721no—
186C24—1721no—
187C24—1722no—
188C24C22×D4311yescharacteristic
189C24C22×D4311yescharacteristic
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—438no—
193C2×D4—1722no—
194C2×D4—1722no—
195C2×D4C4×D4314yes—
196C22×C4—42no—
197C22×C4—41no—
198C22×C4—432no—
199C22×C4—432no—
200C22×C4—432no—
201C22×C4C22×D4312yes—
202C22×C4C22×D4312yes—
203C22×C4C22×D4311yescharacteristic
204C4⋊C4—1722no—
205C4⋊C4—1721no—
206C22⋊C4—42no—
207C22⋊C4—41no—
208C22⋊C4—434no—
209C22⋊C4—438no—
210C22⋊C4—1722no—
211C22⋊C4—1722no—
212C22⋊C4—1722no—
213C22⋊C4—1722no—
214C22⋊C4—1722no—
215C22⋊C4—1722no—
216C42—1721no—
217C42—1722no—
218C23—21no—
219C23—22no—
220C23—21no—
221C23—22no—
222C23—21no—
223C23—21no—
224C23—22no—
225C23—22no—
226C23—434no—
227C23—862no—
228C23—862no—
229C23—862no—
230C23—862no—
231C23—862no—
232C23—862no—
233C23—1728no—
234C23—1724no—
235C23—1728no—
236C23—1724no—
237C23—1724no—
238C23C2×C4×D4312yes—
239C23C2×C4×D4312yes—
240C23C23×D4311yescharacteristic
241D4—44no—
242D4—1728no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—44no—
252C2×C4—434no—
253C2×C4—862no—
254C2×C4—862no—
255C2×C4—862no—
256C2×C4—862no—
257C2×C4—862no—
258C2×C4—862no—
259C2×C4—862no—
260C2×C4—862no—
261C2×C4C2×C4×D4312yes—
262C22—24no—
263C22—24no—
264C22—22no—
265C22—22no—
266C22—42no—
267C22—42no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—864no—
273C22—864no—
274C22—864no—
275C22—17216no—
276C22—1722no—
277C22—1722no—
278C22—1722no—
279C22—1722no—
280C22C22×C4×D4311yescharacteristic
281C22#1306337012yes—
282C22#1306337011yescharacteristic
283C22#1306337011yescharacteristic
284C22#1306337112yes—
285C4—22no—
286C4—42no—
287C4—42no—
288C4—864no—
289C4—1722no—
290C4—1722no—
291C2—42no—
292C2—42no—
293C2—1724no—
294C2#1458337112yes—
295C2#1458337211yescharacteristic
296C2#1458363712yes—
297C2#1458363911yescharacteristic
298C2#1458364211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC43×#386C2
socleC23×C43C24
hypercenter#386D43
hypocenterC43#2375
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #386

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14582802C2semidirect
3. #14582799C2semidirect
4. #14582793C2semidirect
5. #14582791C2semidirect
6. #14582788C2semidirect
7. #14582778C2semidirect
8. #14582754C2semidirect
9. C43×#386C2semidirect
12. #13063293C4semidirect
13. C2×C4⋊Dic43C22semidirect
14. C2×Dic43⋊C4C22semidirect
17. C2×C22⋊Dic43C22semidirect
23. C2×C4×Dic43C22semidirect
24. C2×C4×Dic43C22semidirect
25. C43⋊#95C22semidirect
26. C43⋊#95C22semidirect
28. C23×C4×C43C22semidirect
30. C2×C22⋊C4×C43C22semidirect
31. #95×C43C22semidirect
38. C23×D43C2×C4semidirect
58. C22⋊Dic43C2×C4semidirect
63. (C2×D43)⋊C4C2×C4semidirect
157. #386D43semidirect
159. C43#2375semidirect
163. C23×C4C2×D43semidirect
176. C2×C22⋊C4C2×D43semidirect
181. #95C2×D43semidirect